Symbol Definition Units
\(f\ (subscript)\) Fluid phase -
\(m\ (subscript)\) Matrix phase -
\(n\ (subscript)\) Experiment index -
\(n\) (superscript) Grain size dependence exponent -
\(t\) Time \(s\)
\(V\) Volume \(m^{3}\)
\(\rho\) Density \(\text{kg\ m}^{-3}\)
\(A\) Area \(m^{2}\)
\(v\) Velocity \(\text{m\ s}^{-1}\)
\(z\) Depth \(g\)
\(\sigma\) Total stress tensor Pa
\(g\) Gravitational constant \(\text{m\ }s^{-2}\)
\(H\) Interfacial traction tensor Pa
\(c_{1}\) Drag coefficient \(\text{Pa\ s\ }m^{-2}\)
\(P\) Thermodynamic pressure Pa
\(\eta_{f}\) Dynamic viscosity of fluid Pa s
d Grain size (diameter) mm or μm
\(\kappa\) Matrix permeability \(m^{2}\)
\(\tau\) Viscous stress tensor Pa
\(\pi\) Geometric constant -
\(\eta\) Matrix shear viscosity Pa s
\(\eta_{s}\) Matrix shear viscosity as \(\phi\ \rightarrow 0\) Pa s
\(K\) Matrix bulk viscosity Pa s
\(f_{\eta}\) Shear viscosity dependence on \(\phi\) -
\(f_{K}\) Bulk viscosity dependence on \(\phi\) -
\(\mathbf{v}_{\mathbf{0}}\) Reference velocity \(\text{m\ }s^{-1}\)
\(v_{H}\) Boundary velocity \(\text{m\ }s^{-1}\)
\(S\) Segregation velocity \(\text{m\ }s^{-1}\)
\(y\) Unitless depth -
\(H\) Height of compacting domain \(m\)
\(H_{0}\) Initial height of compacting domain \(m\)
\(\xi\) Effective matrix viscosity Pa s
\(\xi_{\text{ref}}\) Reference viscosity Pa s
\(\phi\) Porosity or melt fraction -
\(\phi_{m}\) Maximum packing fraction -
\(\phi_{\text{dis}}\) Disaggregation melt fraction -
\(\mu_{\text{friction}}\) Friction coefficient -
\(\sum\ \) Applied stress on piston Pa
\(d\) Displacement mm
\(\zeta\) \(\frac{\text{πξ}}{\phi}\) Pa s
\(c\) \(\frac{\eta_{f}\phi^{2}}{\kappa}\) \(\frac{\text{Pa\ s}}{m^{2}}\)
\(\beta\) \(\frac{c}{\phi^{2}}\) \(\frac{\text{Pa\ s}}{m^{2}}\)
\(\delta_{c}\) Compaction length \(m\)
\(L_{0}\) Misfit \(\text{Pa}^{2}\) or unitless
\(\Pi\) Observed data Pa or unitless
\(\vartheta\) Model Pa or unitless
\(m\) Vector of model parameters Mixed
\(N\) # of MCMC iterations -
\(\mu[\ ]\) Mean of posterior distribution of given parameter -
\(\sigma[\ ]\) Standard deviation of posterior distribution of given parameter -